Signatures of Reaction Mechanisms Encoded in the Vibrational Population Distribution of Small-Molecule Products: Photodissociation of Symmetric-Triazine Using 266 nm Radiation.

We utilize rotationally resolved Chirped-Pulse Fourier Transform millimeter-wave spectroscopy to study photodissociation dynamics of 1,3,5-Triazine (symmetric-Triazine) to form 3 HCN molecules. The state-specific vibrational population distribution (VPD) of the photofragments contains mechanistic details of the reaction. This photodissociation is performed using 266 nm radiation transverse to a seeded supersonic jet. The vibrational cooling inefficiency in the jet preserves the VPD of the photofragments, while rotational cooling enhances the signal of low-J pure-rotational transitions. The multiplexed nature of the spectrometer enables simultaneous sampling of several "vibrational satellites" of the J = 1 ← 0 transition of HCN. Excited state populations along the HCN bend (v2) and CN stretch (v3) modes are observed, which show ≥3.2% vibrational excitation of the photofragments. Observation of an at least bimodal VPD, along the even-v states of v2, implies an asymmetric partitioning of vibrational energy among the HCN photofragments. This suggests a sequential dissociation mechanism of symmetric-Triazine initiated by 266 nm radiation.

VUV-VIS FT spectroscopy of the rare 13C18O isotopologue of carbon monoxide: Analysis of the A1Π(v = 1) multiply-perturbed level.

Ro-vibronic spectra of the 13C18O carbon monoxide isotopologue were obtained with (i) emission spectroscopy in the visible region using a Bruker IFS 125HR spectrometer (University of Rzeszów) and (ii) vacuum-ultraviolet absorption spectroscopy using the wave-front-division spectrometer on the DESIRS beamline of the SOLEIL synchrotron. A deperturbation analysis of the 13C18O A1Π(v = 1) level was conducted from 598 observed transitions from the B1Σ+ - A1Π(0, 1), C1Σ+ - A1Π(0, 1), A1Π - X1Σ+(1, 0), B1Σ+ - X1Σ+(0, 0), C1Σ+ - X1Σ+(0, 0), I1Σ- - X1Σ+(2, 0) bands and five further nominally forbidden bands. An effective Hamiltonian and term-value fitting analysis was implemented. Consequently, 135 parameters were floated: 23 molecular parameters, including molecular constants for A1Π(v = 1), I1Σ-(v = 2), d3Δ(v = 6), e3Σ-(v = 3) and D1Δ(v = 1); rotation-electronic (L-uncoupling) mixing of A1Π(v = 1) âˆ¼ [D1Δ(v = 1), I1Σ-(v = 1), I1Σ-(v = 2)] and spin-orbit interaction parameters for A1Π(v = 1) âˆ¼ [d3Δ(v = 6), e3Σ-(v = 3), a'3Σ+(v = 11)]; the spin-orbit/spin-electronic/L-uncoupling a3Π(v = 12) âˆ¼ d3Δ(v = 5) and spin-orbit a3Π(v = 12) âˆ¼ [D1Δ(v = 1), I1Σ-(v = 2)] perturbation parameters; as well as 112 ro-vibronic term values of B1Σ+(v = 0) up to J = 50 and C1Σ+(v = 0) up to J = 60. The significant, indirect a3Π(v = 12) âˆ¼ [e3Σ-(v = 2, 3), d3Δ(v = 5, 6)] âˆ¼ A1Π(v = 1) spin-orbit/spin-electronic/L-uncoupling interaction and a3Π(v = 12) âˆ¼ [I1Σ-(v = 2), D1Δ(v = 1)] âˆ¼ A1Π(v = 1) spin-orbit/L-uncoupling interaction were detected and analysed. Thus, this study, using modern experimental methods and deperturbation analysis, leads to a much improved description in terms of molecular constants and interaction parameters, compared to previous studies of the A1Π(v = 1) energy region in the 13C18O isotopologue. This research is a continuation of the studies on the A1Π state and its numerous perturbers in the CO isotopologues made by our team.

Diabatic Valence-Hole States in the C2 Molecule: "Putting Humpty Dumpty Together Again".

Despite the long history of spectroscopic studies of the C2 molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C2 is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions that occur within four symmetry manifolds of excited states of C2 (1Πg, 3Πg, 1Σu+ , and 3Σu+ ). The key concept of our model is the existence of two "valence-hole" configurations, 2σg22σu11πu33σg2 for 1,3Πg states and 2σg22σu11πu43σg1 for 1,3Σu+ states, that are derived from 3σg ← 2σu electron promotion. The lowest-energy state from each of the four C2 symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s22p2 + 2s2p3 separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the global electronic structure and unimolecular dynamics of C2.

Theory of oil fouling for microfiltration and ultrafiltration membranes in produced water treatment.

Due to the complexity of oil-in-water emulsions, the existing literature is still missing a mathematical tool that can describe membrane fouling in a fully quantitative manner on the basis of relevant fouling mechanisms. HYPOTHESIS: In this work, a quantitative model that successfully describes cake layer formation and pore blocking is presented. We propose that the degree of pore blocking is determined by the membrane contact angle and the resulting surface coverage, while the cake layer is described by a mass balance and a cake erosion flux. VALIDATION: The model is validated by comparison to experimental data from previous works (Dickhout et al. 2019; Virga et al., 2020) where membrane type, surfactant type and salinity were varied. Most input parameters could be directly taken from the experimental conditions, while four fitting parameters were required. FINDINGS: The experimental data can be well described by the model which was developed to provide insight into the dominant fouling mechanisms. Moreover, where existing models usually assume that pore blocking precedes cake layer formation, here we find that cake layer formation can start and occur while the degree of pore blocking is still increasing, in line with the more dynamic nature of oil droplets filtration. These new conceptual advances in the field of colloid and interface science open up new pathways for membrane fouling understanding, prevention and control.

Permeate Flux in Ultrafiltration Processes-Understandings and Misunderstandings.

Concentration polarization refers to the rapid emergence of concentration gradients at a membrane/solution interface resulting from selective transfer through the membrane. It is distinguishable from fouling in at least two ways: (1) the state of the molecules involved (in solution for concentration polarization, although no longer in solution for fouling); and (2) by the timescale, normally less than a minute for concentration polarization, although generally at least two or more orders of magnitude more for fouling. Thus the phenomenon of flux decline occurring over a timescale of tens of minutes should not be attributed to concentration polarization establishing itself. This distinction and a number of questions surrounding modelling are addressed and clarified. There are two paradigmatic approaches for modelling flux, one uses the overall driving force (in which case allowance for osmotic effects are expressed as additional resistances) and the other uses the net driving force across the separating layer or fouled separating layer, although often the two are unfortunately comingled. In the discussion of flux decline models' robust approaches for the determination of flux-time relationships, including the integral method of fouling analysis, are discussed and various concepts clarified. The final section emphases that for design purposes, pilot plant data are vital.

Photodissociation of dicarbon: How nature breaks an unusual multiple bond.

The dicarbon molecule (C2) is found in flames, comets, stars, and the diffuse interstellar medium. In comets, it is responsible for the green color of the coma, but it is not found in the tail. It has long been held to photodissociate in sunlight with a lifetime precluding observation in the tail, but the mechanism was not known. Here we directly observe photodissociation of C2 From the speed of the recoiling carbon atoms, a bond dissociation energy of 602.804(29) kJ·mol[Formula: see text] is determined, with an uncertainty comparable to its more experimentally accessible N2 and O2 counterparts. The value is within 0.03 kJ·mol-1 of high-level quantum theory. This work shows that, to break the quadruple bond of C2 using sunlight, the molecule must absorb two photons and undergo two "forbidden" transitions.

Nonlinear rotational spectroscopy reveals many-body interactions in water molecules.

Because of their central importance in chemistry and biology, water molecules have been the subject of decades of intense spectroscopic investigations. Rotational spectroscopy of water vapor has yielded detailed information about the structure and dynamics of isolated water molecules, as well as water dimers and clusters. Nonlinear rotational spectroscopy in the terahertz regime has been developed recently to investigate the rotational dynamics of linear and symmetric-top molecules whose rotational energy levels are regularly spaced. However, it has not been applied to water or other lower-symmetry molecules with irregularly spaced levels. We report the use of recently developed two-dimensional (2D) terahertz rotational spectroscopy to observe high-order rotational coherences and correlations between rotational transitions that were previously unobservable. The results include two-quantum (2Q) peaks at frequencies that are shifted slightly from the sums of distinct rotational transitions on two different molecules. These results directly reveal the presence of previously unseen metastable water complexes with lifetimes of 100 ps or longer. Several such peaks observed at distinct 2Q frequencies indicate that the complexes have multiple preferred bimolecular geometries. Our results demonstrate the sensitivity of rotational correlations measured in 2D terahertz spectroscopy to molecular interactions and complexation in the gas phase.

Substitution Reactions in the Pyrolysis of Acetone Revealed through a Modeling, Experiment, Theory Paradigm.

The development of high-fidelity mechanisms for chemically reactive systems is a challenging process that requires the compilation of rate descriptions for a large and somewhat ill-defined set of reactions. The present unified combination of modeling, experiment, and theory provides a paradigm for improving such mechanism development efforts. Here we combine broadband rotational spectroscopy with detailed chemical modeling based on rate constants obtained from automated ab initio transition state theory-based master equation calculations and high-level thermochemical parametrizations. Broadband rotational spectroscopy offers quantitative and isomer-specific detection by which branching ratios of polar reaction products may be obtained. Using this technique, we observe and characterize products arising from H atom substitution reactions in the flash pyrolysis of acetone (CH3C(O)CH3) at a nominal temperature of 1800 K. The major product observed is ketene (CH2CO). Minor products identified include acetaldehyde (CH3CHO), propyne (CH3CCH), propene (CH2CHCH3), and water (HDO). Literature mechanisms for the pyrolysis of acetone do not adequately describe the minor products. The inclusion of a variety of substitution reactions, with rate constants and thermochemistry obtained from automated ab initio kinetics predictions and Active Thermochemical Tables analyses, demonstrates an important role for such processes. The pathway to acetaldehyde is shown to be a direct result of substitution of acetone's methyl group by a free H atom, while propene formation arises from OH substitution in the enol form of acetone by a free H atom.

Long-range model of vibrational autoionization in core-nonpenetrating Rydberg states of NO.

In high orbital angular momentum (ℓ ≥ 3) Rydberg states, the centrifugal barrier hinders the close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-ℓ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular momentum exchange between the ion-core and the Rydberg electron that had been previously observed in vibrational autoionization of f (ℓ = 3) Rydberg states. These results shed light on a long-standing mechanistic question around these previous observations and support a direct, vibrational mechanism of autoionization over an indirect, predissociation-mediated mechanism. In addition, our model correctly predicts newly measured total decay rates of g (ℓ = 4) Rydberg states because for ℓ ≥ 4, the non-radiative decay is dominated by autoionization rather than predissociation. We examine the predicted NO+ ion rotational state distributions generated by vibrational autoionization of g states and discuss applications of our model to achieve quantum state selection in the production of molecular ions.

Photodissociation transition states characterized by chirped pulse millimeter wave spectroscopy.

The 193-nm photolysis of CH2CHCN illustrates the capability of chirped-pulse Fourier transform millimeter-wave spectroscopy to characterize transition states. We investigate the HCN, HNC photofragments in highly excited vibrational states using both frequency and intensity information. Measured relative intensities of J = 1-0 rotational transition lines yield vibrational-level population distributions (VPD). These VPDs encode the properties of the parent molecule transition state at which the fragment molecule was born. A Poisson distribution formalism, based on the generalized Franck-Condon principle, is proposed as a framework for extracting information about the transition-state structure from the observed VPD. We employ the isotopologue CH2CDCN to disentangle the unimolecular 3-center DCN elimination mechanism from other pathways to HCN. Our experimental results reveal a previously unknown transition state that we tentatively associate with the HCN eliminated via a secondary, bimolecular reaction.

The frequency-domain infrared spectrum of ammonia encodes changes in molecular dynamics caused by a DC electric field.

Ammonia is special. It is nonplanar, yet in v = 1 of the umbrella mode (ν2) its inversion motion is faster than J = 0↔1 rotation. Does the simplicity of the Chemist's concept of an electric dipole moment survive the competition between rotation, inversion, and a strong external electric field? NH3 is a favorite pedagogical example of tunneling in a symmetric double-minimum potential. Tunneling is a dynamical concept, yet the quantitative characteristics of tunneling are expressed in a static, eigenstate-resolved spectrum. The inverting-umbrella tunneling motion in ammonia is both large amplitude and profoundly affected by an external electric field. We report how a uniquely strong (up to 108 V/m) direct current (DC) electric field causes a richly detailed sequence of reversible changes in the frequency-domain infrared spectrum (the v = 0→1 transition in the ν2 umbrella mode) of ammonia, freely rotating in a 10 K Ar matrix. Although the spectrum is static, encoded in it is the complete inter- and intramolecular picture of tunneling dynamics.

On the understanding and feasibility of "Breakthrough" Osmosis.

Osmosis is the movement of solvent across a permselective membrane induced by a solute-concentration gradient. Now in 'Forward Osmosis' it is empirically observed that the diffusion of the solute is counter to that of the solvent i.e. there is so-called "reverse salt diffusion". However it has been recently suggested, in a theoretical paper, that if allowance is made for minor deviations from ideal semi-permeability then operation in an overlooked mode of "breakthrough" osmosis would be possible and importantly it would yield relatively large rates of osmosis. A consequential prediction was that in "breakthrough mode", Pressure-Retarded Osmosis (PRO) would generate very high power densities exceeding those in the conventional mode by one order of magnitude. The practicality of this suggestion was explored and necessarily questions were then raised regarding the foundation of the Spiegler-Kedem-Katchalsky model.Arising from: Yaroshchuk, A., Sci. Rep. 7, 45168 (2017); https://doi.org/10.1038/srep45168.

Analysis of vibrational autoionization of CaF Rydberg states.

We report calculations of vibrational autoionization rates of CaF Rydberg states, based on the results of a global multi-channel quantum defect theory (MQDT) fit. Our goal is to use intuitive physical models to interpret and extend the results from the MQDT calculations and, in particular, to characterize the physical mechanisms for the interaction between the Rydberg electron and the ion-core. The calculations indicate that, among the six strongly l-mixed core-penetrating (CP) Rydberg series of CaF, the n.36 p^Π Rydberg series has the fastest Δv = 1 vibrational autoionization rate, which is at least four times larger than that for the other CP Rydberg series, in agreement with experimental results. We first demonstrate that the rotational level dependence of the vibrational autoionization rate of the n.36 p^Π series is satisfactorily explained by l-uncoupling interactions, which differ for the positive and negative Kronig symmetry levels. Next, we interpret the relative vibrational autoionization rates of all six CP Rydberg series in the context of a valence-precursor (VP) model. The VP model is a consequence of Mulliken's rule, which states that the innermost lobe of the Rydberg wavefunction remains invariant in both the nodal position and shape for members of the same Rydberg series. The electronic properties of the six VP states, which are the terminus states (lowest-n) of each of the six CP Rydberg series, are further characterized in terms of a ligand-field model, providing insight into the intimate relationship between the Rydberg electron density in the ion-core region and the vibrational autoionization rate.

Probing the predissociated levels of the S1 state of acetylene via H-atom fluorescence and photofragment fluorescence action spectroscopy.

We report two new experimental schemes to obtain rotationally resolved high-resolution spectra of predissociated S1 acetylene levels in the 47 000-47 300 cm-1 energy region (∼1200 cm-1 above the predissociation threshold). The two new detection schemes are compared to several other detection schemes (employed at similar laser power, molecular beam temperature, and number of signal averages) that have been used in our laboratory to study predissociated S1 acetylene levels, both in terms of the signal-to-noise ratio (S/N) of the resultant spectra and experimental simplicity. In the first method, H-atoms from the predissociated S1 acetylene levels are probed by two-photon laser-induced fluorescence (LIF). The H-atoms are pumped to the 3d level by the two-photon resonance transition at 205.14 nm. The resulting 3d-2p fluorescence (654.5 nm) is collected by a photomultiplier. The S/N of the H-atom fluorescence action spectrum is consistently better by ∼3× than that of the more widely used H-atom resonance-enhanced multiphoton ionization (REMPI) detection. Laser alignment is also considerably easier in H-atom fluorescence detection than H-atom REMPI detection due to the larger number-density of molecules that can be used in fluorescence vs. REMPI detection schemes. In the second method, fluorescence from electronically excited C2 and C2H photofragments of S1 acetylene is detected. In contrast to the H-atom detection schemes, the detected C2 and C2H photofragments are produced by the same UV laser as is used for the à - X ̃ acetylene excitation. As a result, laser alignment is greatly simplified for the photofragment fluorescence detection scheme, compared to both H-atom detection schemes. Using the photofragment fluorescence detection method, we are able to obtain action spectra of predissociated S1 acetylene levels with S/N ∼2× better than the HCCH REMPI detection and ∼10× better than H-atom and HCCH LIF detection schemes.

Coherent laser-millimeter-wave interactions en route to coherent population transfer.

We demonstrate coherent two-photon population transfer to Rydberg states of barium atoms using a combination of a pulsed dye laser and a chirped-pulse millimeter-wave spectrometer. Numerical calculations, using a density matrix formalism, reproduce our experimental results and explain the factors responsible for the observed fractional population transferred, optimal experimental conditions, and possibilities for future improvements. The long coherence times associated with the millimeter-wave radiation aid in creating coherence between the ground state and Rydberg states, but higher-coherence laser sources are required to achieve stimulated Raman adiabatic passage and for applications to molecules.

Encoding of vinylidene isomerization in its anion photoelectron spectrum.

Vinylidene-acetylene isomerization is the prototypical example of a 1,2-hydrogen shift, one of the most important classes of isomerization reactions in organic chemistry. This reaction was investigated with quantum state specificity by high-resolution photoelectron spectroscopy of the vinylidene anions H2CC- and D2CC- and quantum dynamics calculations. Peaks in the photoelectron spectra are considerably narrower than in previous work and reveal subtleties in the isomerization dynamics of neutral vinylidene, as well as vibronic coupling with an excited state of vinylidene. Comparison with theory permits assignment of most spectral features to eigenstates dominated by vinylidene character. However, excitation of the ν6 in-plane rocking mode in H2CC results in appreciable tunneling-facilitated mixing with highly vibrationally excited states of acetylene, leading to broadening and/or spectral fine structure that is largely suppressed for analogous vibrational levels of D2CC.

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states.

The dependence of multipole moments and polarizabilities on external fields appears in many applications including biomolecular molecular mechanics, optical non-linearity, nanomaterial calculations, and the perturbation of spectroscopic signatures in atomic clocks. Over a wide range of distances, distributed multipole and polarizability potentials can be applied to obtain the variation of atom-centered atoms-in-molecules electric properties like bonding-quenched polarizability. For cylindrically symmetric charge distributions, we examine single-center and atom-centered effective polarization potentials in a non-relativistic approximation for Rydberg states. For ions, the multipole expansion is strongly origin-dependent, but we note that origin-independent invariants can be defined. The several families of invariants correspond to optimized representations differing by origin and number of terms. Among them, a representation at the center of dipole polarizability optimizes the accuracy of the potential with terms through 1/r4. We formulate the single-center expansion in terms of polarization-modified effective multipole moments, defining a form related to the source-multipole expansion of Brink and Satchler. Atom-centered potentials are an origin independent alternative but are limited both by the properties allowed at each center and by the neglected effects like bond polarizability and charge flow. To enable comparisons between single-center effective potentials in Cartesian or spherical form and two-center effective potentials with differing levels of mutual induction between atomic centers, we give analytical expressions for the bond-length and origin-dependence of multipole and polarizability terms projected in the multipole and polarizability expansion of Buckingham. The atom-centered potentials can then be used with experimental data and ab initio calculations to estimate atoms-in-molecules properties. Some results are given for BaF+ and HF showing the utility and limitations of the approach. More detailed results on X 1Σ+ CaF+ are published separately.

Saddle point localization of molecular wavefunctions.

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

Perspective: The first ten years of broadband chirped pulse Fourier transform microwave spectroscopy.

Since its invention in 2006, the broadband chirped pulse Fourier transform spectrometer has transformed the field of microwave spectroscopy. The technique enables the collection of a ≥10 GHz bandwidth spectrum in a single shot of the spectrometer, which allows broadband, high-resolution microwave spectra to be acquired several orders of magnitude faster than what was previously possible. We discuss the advantages and challenges associated with the technique and look back on the first ten years of chirped pulse Fourier transform spectroscopy. In addition to enabling faster-than-ever structure determination of increasingly complex species, the technique has given rise to an assortment of entirely new classes of experiments, ranging from chiral sensing by three-wave mixing to microwave detection of multichannel reaction kinetics. However, this is only the beginning. Future generations of microwave experiments will make increasingly creative use of frequency-agile pulse sequences for the coherent manipulation and interrogation of molecular dynamics.